Disk Locked; cannot Re-install Osx

[tomholland2028]

Hello everyone, before encountering the error, I attempted to transfer data from an old Mac to this Mac. However, it encountered errors multiple times and couldn't complete the transfer (it only transferred about 80% of the data from the old machine before stopping). After each instance, I formatted the hard drives to their original state and reinstalled macOS, then continued the data transfer as before. On the third data transfer attempt, after formatting the drives, I had to shut down the computer due to other commitments.

Today, when I turned the computer back on, it displayed a flashing folder icon. I tried pressing cmd + R to format the drive and reinstall OS X, but it didn't work because the drives are locked as shown in the picture. I'm not sure what to do. I hope someone can help. I just need the computer to run normally again, and I don't care about the data inside; there's no need to back it up.

P/s:
To be honest, I'm not familiar with iMacs, so my actions may seem foolish. I hope you can overlook that and guide me.

 

[Satcomer]

What format did you make the external? The using Big Sur or later you must format with newer formate APFS NOT HFS+!

 

[DeltaMac]

Looks like you have a fusion drive.
If you are offered Mountain Lion as an installer when you boot to internet recovery, the newest iMac that shipped with that, is the Late 2013 iMac, which cannot update beyond Catalina (macOS 10.15.7) You can only go to Big Sur or later, with a patched system, That's easy to do, but it's not an install where you just run the installer as it comes.
And, you can't format APFS from a Mountain Lion installer, even if you wanted to do that.
(That Mountain Lion installer that you see won't do anything with an APFS volume, the Mountain Lion system is too old to know what that is.)
Your Disk Utility shows a drive that you are booted to (the Mac OS X Base System). That is what Apple provides to you for internet recovery, and is not actually on your iMac at all, it is just the remote system that you are using. The only drive that you can erase is the one you have named "Internal Drive"
And, HFS+ (also called MacOS Extended (journaled)) is just fine. If you install a newer system that can use APFS format, the installer will automatically make that change for you.